To me it's both.
I prefer a published setting, and have been running my campaign in the Forgotten Realms since it was released in '87. Having said that, I followed directions and have made it my own. To start, it's much closer to the originally released setting in feel and content than the 5e version now. But I also incorporate probably 95%+ of what's been published over the years and we're currently in 1491 DR.
The way I look at it, what the players read is compiled by many people over many years (true really), and the accuracy of such reports vary widely. I take advantage of the fact that the maps have changed over the years, and tweak things as needed. I rarely use a published adventure as is, but frequently pull pieces out to use. It might be a single idea, room, NPC, or encounter, or it might be an entire dungeon, with little or no changes.
Beyond that, there's all of the stuff that I've added and, perhaps more importantly, the stuff the players have added through their characters over the years.
One of the main reasons I prefer a published setting is specifically so the players can read up on whatever they want. NPCs and plots are almost always modified, and it's more important to me that we have an immersive experience than worrying that they read about this or that. The more they know about the world around them, the more alive the world seems to be. It's easy in a setting like Star Wars, because so many people know so much. So nothing is really off limits. Sourcebooks, novels, video games, etc. But they also know that it's not all 100% correct.
Only what actually enters play at the table is canon in the campaign. And player's input is primarily through the actions of their characters, but they also flesh out things like their families, sometimes friends, etc. And in the process that often helps flesh out the world a bit more too. Like who lives where, does what, knows whom because of it, etc. If they happen to be from a more "important" family, such as a noble family, then fleshing out some of the stuff of that family too is expected.
I see it as a collaborative effort, and I offer suggestions, occasional nudges into certain directions, and rarely an outright "no" to what they develop, primarily at character creation. But when they are in their hometown, for example, and encounter a group of people, it's certainly reasonable for them to help define the relationships they have (or not) with that group of people, as a group and individually.
The exact approach does vary depending on the group of players at hand. Some prefer a much more linear DM-authored plot, and I can provide that. But I prefer it to be more player/character driven. Also, because this has been a long-term ongoing campaign, many of the events, and definitely NPCs come from earlier adventures and players. We have a lot of adventurers retire to normal life, and they usually become recurring aspects of the campaign and occasionally "unretire" as the situation warrants.
